Least Common Multiple (LCM) of 140 and 81
The least common multiple (LCM) of 140 and 81 is 11340.
What is the Least Common Multiple (LCM)?
The LCM of two integers is the smallest positive integer that is divisible by both numbers. It is often used to find common denominators and solve problems involving periodic events.
Formula for LCM
The LCM of two numbers can be calculated using their GCD:
LCM(a, b) = |a × b| ÷ GCD(a, b)
How to Calculate the LCM of 140 and 81?
First, calculate the GCD of 140 and 81 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 140 ÷ 81 = 1 remainder 59 |
| 2 | 81 ÷ 59 = 1 remainder 22 |
| 3 | 59 ÷ 22 = 2 remainder 15 |
| 4 | 22 ÷ 15 = 1 remainder 7 |
| 5 | 15 ÷ 7 = 2 remainder 1 |
| 6 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 18 and 142 | 1278 |
| 43 and 175 | 7525 |
| 43 and 125 | 5375 |
| 166 and 135 | 22410 |
| 112 and 168 | 336 |